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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: The philosophy of logic reformulates existing ideas on a new
 basis --- infallibly correct
Date: Sun, 10 Nov 2024 23:03:12 -0500
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On 11/10/24 10:07 PM, olcott wrote:
> On 11/10/2024 4:19 PM, Alan Mackenzie wrote:
>> olcott <polcott333@gmail.com> wrote:
>>> On 11/10/2024 2:36 PM, Alan Mackenzie wrote:
>>>> olcott <polcott333@gmail.com> wrote:
>>>>> On 11/10/2024 1:04 PM, Alan Mackenzie wrote:
>>
>>>> [ .... ]
>>
>>>>>> I have addressed your point perfectly well.  Gödel's theorem is 
>>>>>> correct,
>>>>>> therefore you are wrong.  What part of that don't you understand?
>>
>>>>> YOU FAIL TO SHOW THE DETAILS OF HOW THIS DOES
>>>>> NOT GET RID OF INCOMPLETENESS.
>>
>>>> The details are unimportant.  Gödel's theorem is correct.
>>
>>> In other words you simply don't understand these
>>> things well enough ....
>>
>> Not at all.  It's you that doesn't understand them well enough to make it
>> worthwhile trying to discuss things with you.
>>
>>> .... to understand that when we change their basis the conclusion
>>> changes.
>>
>> You're at too high a level of abstraction.  When your new basis has
>> counting numbers, it's either inconsistent, or Gödel's theorem applies to
>> it.
>>
> 
> Finally we are getting somewhere.
> You know what levels of abstraction are.
> 
>>> You are a learned-by-rote guy that accepts what you
>>> memorized as infallible gospel.
>>
>> You're an uneducated boor.  So uneducated that you don't grasp that
>> learning by rote simply doesn't cut it at a university.
>>
>>>> Your ideas contradict that theorem.
>>
>>> When we start with a different foundation then incompleteness
>>> ceases to exist just like the different foundation of ZFC
>>> eliminates Russell's Paradox.
>>
>> No.  You'd like it to, but it doesn't work that way.
>>
>> [ .... ]
>>
>>>> Therefore your ideas are incorrect.  Again, the precise details are
>>>> unimportant,
>>
>>> So you have no clue how ZFC eliminated Russell's Paradox.
>>> The details are unimportant and you never heard of ZFC
>>> or Russell's Paradox anyway.
>>
>> Russell's paradox is a different thing from Gödel's theorem.  The latter
>> put to rest for ever the vainglorious falsehood that we could prove
>> everything that was true.
>>
> 
> Ah so you don't understand HOW ZFC eliminated Russell's Paradox.
> 
> We can ALWAYS prove that any expression of language is true or not
> on the basis of other expressions of language when we have a coherent
> definition of True(L,x).

No, we can't.

We can sometimes prove it is true if we can find the sequence of steps 
that establish it.

We can sometime prove it is false if we can find the sequence of steps 
that refute it.

Since there are potentially an INFINITE number of possible proofs for 
either of these until we find one of them, we don't know if the 
statement IS provable or refutable.

Your problem is you think that knowledge and truth are the same, but 
knowledge is only a subset of truth, and there are unknown truths, and 
even unknowable truths in any reasonably complicated system.

Part of your issue is you seem to only think in very simple systems 
where exhaustive searching might actually be viable.

> 
> That Gödel relies on True(meta-math, g) to mean True(PA, g)
> is a stupid mistake that enables Incomplete(PA) to exist.
> 
> 

Which just shows you don't understand how formal systems, and their 
meta-systems are constructed.

Your ignorance doesn't make the claim not true, just shows that you are 
just stupid and a pathological liar.